Solve {l}{2+6=m+n}{3+1=0+6/n}

$$\left\{ \begin{array} { l } { 2 + 6 = m + n } \\ { 3 + 1 = 0 + \frac { 6 } { n } } \end{array} \right.$$

Solve for m, n

$$m = \frac{13}{2} = 6\frac{1}{2} = 6.5$$

$$n = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Solution Steps

Consider the second equation. Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n.

$$n\times 3+n=0+6$$

Combine n\times 3 and n to get 4n.

$$4n=0+6$$

Add 0 and 6 to get 6.

$$4n=6$$

Divide both sides by 4.

$$n=\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$n=\frac{3}{2}$$

Consider the first equation. Insert the known values of variables into the equation.

$$2+6=m+\frac{3}{2}$$

Add 2 and 6 to get 8.

$$8=m+\frac{3}{2}$$

Swap sides so that all variable terms are on the left hand side.

$$m+\frac{3}{2}=8$$

Subtract \frac{3}{2} from both sides.

$$m=8-\frac{3}{2}$$

Subtract \frac{3}{2} from 8 to get \frac{13}{2}.

$$m=\frac{13}{2}$$

The system is now solved.

$$m=\frac{13}{2} n=\frac{3}{2}$$